Problem 1 - Finite Automaton

For a string $x=x_{n-1}\cdots x_1 x_0 \in \{0,1\}^*$ $(x_i\in\{0,1\},i=0,\dots,n-1)$, we define an integer $[x]$ by $[x] = x_{n-1}2^{n-1} + \cdots + x_12^1 + x_02^0$, where $[\epsilon] = 0$. Show that the language

$$L=\{x\in\{0,1\}^*\;\vert\;[x]=3n\;\hbox{for some integer}\;n\geq 0\}$$

is accepted by a finite automaton.